A test of time dilation with an optical atomic clock on a stratospheric balloon

最先进的光学晶格钟的性能为改进广义相对论的基本效应之一——引力势中的时间膨胀——提供了一个机会。对这种效应最精确的测试是在40年前进行的，通过比较两个微波时钟在1万公里高度上的差异。对这种效应进行一种新的、非卫星的、具有竞争性精度的测试，必然意味着需要在实验室之外操作一个光学时钟。在此，我们建议建造一个镱光学晶格时钟，并将其作为探测时钟在重要高度上使用，通过与地面参考时钟的频率比较来精确测量引力时间膨胀。我们的目标是测量精度优于即将到来的太空任务ACES (2017-18)， ACES使用冷原子Cs微波时钟。为了实现该项目的目标，我们建议开发一种可飞行的光学时钟（FOC），这是一种特别紧凑和坚固的设备，它还首次包含两个原子子系统，允许深入表征和优化我们特定实验的性能。为了放宽对探针和参考时钟的精度要求，在我们的应用中，我们预计在每次实验期间，它们首先在地面上进行比较，然后将FOC带到高度并重复比较。因此，主要要求是FOCs的再现性和参考频率。此外，为了最小化持续时间有限的测量过程中的集成时间，实现高频率稳定性至关重要。在一个长达7年的项目中，我们计划进行越来越复杂的实验，包括垂直距离和两个时钟之间的联系。在演示实验（4年级）中，FOC将在<s:1>塞尔多夫电视塔的全景层运行，距离地面参考时钟160米，通过光纤链路连接并相互比较。这将提供一个在1E-3水平上的引力时间膨胀的测试。在项目的最后阶段（第7年），将执行一项任务，其中FOC将在35公里高度的平流层气球上运行约10小时。用于与地面参考时钟进行比较的频率链路将是基于频率梳的双向自由空间激光链路，将在4-6年与NIST和ViaLight的同事合作实施。通过将FOC和参考时钟频率差的统计不确定度平均到2E-18的水平，我们的目标是测量引力时间膨胀，相对不确定度为5E-7，大约比ACES任务的预期目标好4倍。

The performance of state-of-the-art optical lattice clocks offers an opportunity for an improved test of one of the fundamental effects of General Relativity, the time dilation in the gravitational potential. The most precise test of this effect was performed 40 years ago by comparing two microwave clocks on a 10 000 km height difference. A new, non-satellite test of this effect with a competitive precision necessarily implies the need to operate an optical clock outside of the laboratory. Here we propose to build a ytterbium optical lattice clock and to use it as a probe clock on significant altitudes to precisely measure the gravitational time dilation through a frequency comparison with a reference clock on the ground. We aim at a precision of the measurement better than that of the upcoming space mission ACES (2017-18), which employs a cold-atom Cs microwave clock. To achieve the goals of the project, we propose to develop a flyable optical clock (FOC), a particularly compact and robust apparatus, which additionally comprises, for the first time, two atomics subsystems, allowing for in-depth characterization and optimization of performance towards our specific experiment. In order to relax the requirement of accuracy for both the probe and the reference clock, in our application we foresee that during each experiment they are first compared on ground, before the FOC is brought to altitude and the comparison is repeated. Thus, the main requirement is the reproducibility of the FOCs and the references frequency. Furthermore, achieving high frequency stability is crucial in order to minimize the integration time during the measurement campaign, whose duration is limited. In a 7-year long project, we plan to perform experiments of increasing complexity, concerning both the vertical distance and the link between the two clocks. In a demonstration experiment (year 4), the FOC will be operated in the panoramic level of the television tower in Düsseldorf, 160 m above the reference clock on ground, which is connected through a fiber link and intercompared. This will provide a test of the gravitational time dilation at the 1E-3 level. In the final part of the project (years 7), a mission will be performed in which the FOC will be operated on a stratospheric balloon at an altitude of 35 km for approximately 10 hours. The frequency link for comparison with the reference clock on ground will be a frequency-comb-based two-way free-space laser link, to be implemented in collaboration with colleagues from NIST and ViaLight in years 4-6. By averaging down the statistical uncertainty of the frequency difference of the FOC and reference clock to the 2E-18 level, we aim for a measurement of the gravitational time dilation with relative uncertainty of 5E-7, approximately a factor of 4 better than the expected goal of the ACES mission.